1 Answer
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I can now confirm that your influence lowers each day at the income tally (just like lowered Templar influence in unconquered cities goes back up), but it's only a few percent if you have assassins stationed in the city. Even if you control every city, it looks as though it should be trivial to keep them all maxed out if you just keep an eye on them.

Note that your maximum influence percentage appears to be based on the number and level of assassins you have assigned to that city - you'll need 5 high level assassins to reach 100% influence, but once you do it'll take forever for it to decay.